Score : $300$ points

Problem Statement

There is a tree $T$ with $N$ vertices. The $i$-th edge $(1\leq i\leq N-1)$ connects vertex $U_i$ and vertex $V_i$.

You are given two different vertices $X$ and $Y$ in $T$. List all vertices along the simple path from vertex $X$ to vertex $Y$ in order, including endpoints.

It can be proved that, for any two different vertices $a$ and $b$ in a tree, there is a unique simple path from $a$ to $b$.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq X,Y\leq N$
• $X\neq Y$
• $1\leq U_i,V_i\leq N$
• All values in the input are integers.
• The given graph is a tree.

Input

The input is given from Standard Input in the following format:

$N$ $X$ $Y$

$U_1$ $V_1$

$U_2$ $V_2$

$\vdots$

$U_{N-1}$ $V_{N-1}$

Output

Print the indices of all vertices along the simple path from vertex $X$ to vertex $Y$ in order, with spaces in between.

5 2 5
1 2
1 3
3 4
3 5

2 1 3 5

The tree $T$ is shown below. The simple path from vertex $2$ to vertex $5$ is $2$ $\to$ $1$ $\to$ $3$ $\to$ $5$. Thus, $2,1,3,5$ should be printed in this order, with spaces in between.

6 1 2
3 1
2 5
1 2
4 1
2 6

1 2

The tree $T$ is shown below.